Fuzzy Modeling of Labeled Point Cloud Superposition for the Comparison of Protein Binding Sites

Geometric objects are often represented approximately in terms of a finite set of points in three-dimensional Euclidean space. In this paper, we extend this representation to what we call labeled point clouds. A labeled point cloud is a finite set of points, where each point is not only associated with a position in three-dimensional space, but also with a discrete class label that represents a specific property. This type of model is especially suitable for modeling biomolecules such as proteins and protein binding sites, where a label may represent an atom type or a physicochemical property. Proceeding from this representation, we address the question of how to compare two labeled points clouds in terms of similarity. Using fuzzy modeling techniques, we develop a suitable similarity measure as well as an efficient evolutionary algorithm to compute it. Finally, an application study is presented in which the approach is used to classify protein binding sites. Keywords— structural bioinformatics, proteins, similarity, classi-